Answer: It is well-known that according to Torah law, every day begins from the previous night. Thus, Shabbat begins from the time of sunset on Friday evening until the emergence of the stars (nightfall) of Saturday night, which is actually the night belonging to Sunday.
The time of “emergence of the stars” is indeed the halachic time which determines the end of the current day and the beginning of the next day regarding most Torah laws including the end of Shabbat, i.e. one may not perform work following Shabbat until the “emergence of the stars.” When the stars emerge, Shabbat has officially ended and the night belonging to Sunday has begun.
The Dispute Between the Geonim and Rabbeinu Tam
There is a tremendous disagreement among the Rishonim regarding the time of the “emergence of the stars.” According to the Geonim (the leading sages in the generation following the end of the Talmudic era) the time of the “emergence of the stars” is thirteen-and-a- half minutes after sunset. According to Rabbeinu Tam, the “emergence of the stars” is much later, seventy-two minutes after sunset. (Both of these times are calculated as seasonal minutes calculated based on the length of the specific day and not regular minutes.)
The Custom in Israel
The prevalent custom in Israel and many of its surrounding countries has always been to calculate the “emergence of the stars” in accordance with the opinion of the Geonim, i.e. to recite Havdala at approximately thirteen-and-a-half minutes after sunset (a few extra minutes must be added due to the law of “adding onto Shabbat,” i.e. until approximately twenty minutes after sunset, see Responsa Yabia Omer, Volume 7, Chapter 41) and following Havdala, work is customarily permitted to be performed, for Shabbat has already ended. This is indeed the time customarily printed in most calendars today as “nightfall/the emergence of the stars” (however, many ornate calendars on the market today also print the time of nightfall according to Rabbeinu Tam as well).
Halachically Speaking
Indeed, were the Halacha to be decided against the opinion of Rabbeinu Tam because most or all of the Poskim disagree with his words, there would not be much room to be concerned with his opinion as we rule on matters of Halacha based on the rules handed down to us from generation to generation. Regarding this matter, however, this is not the case, for many great Rishonim write that the Halacha follows the opinion of Rabbeinu Tam. According to this opinion, if one performs work on Motza’ei Shabbat before this time, one is liable for death by stoning (for Shabbat desecration is punishable by stoning). This is indeed the opinion of such great Rishonim as Rabbeinu Hai Gaon, Ra’avad, Razah, Ra’ah, Ritba, Ran, Magid Mishneh, Meiri, Ohel Moe’d, Samag, Roke’ach, Mordechi, Rabbeinu Peretz, Rosh, and Rabbeinu Yerocham, among others. This is especially true since Maran Ha’Shulchan Aruch and the Rama rule likewise, as do the Mabit, Radbaz, and Rabbeinu Chaim Abulafia.
The Words of Rabbeinu Yaakov Faragi
Approximately three-hundred years ago, Hagaon Harav Yaakov Faragi (one of the greatest Egyptian Poskim and friend of Rabbeinu Avraham Ha’Levi, author of Ginat Veradim) wrote a pamphlet proving that the Halacha indeed follows the opinion of Rabbeinu Tam and not what is customary in most Jewish communities.
However, in his times, the Jewish community in Egypt did not follow the opinion of Rabbeinu Tam at all and Rabbeinu Yaakov Faragi was hesitant to publicize this work. At the end of his response, he writes as follows: “At present, I have delved into this matter for more than fifty years and have tried to promote this innocently (he wished to implement the time of Rabbeinu Tam and no one listened to him); even my wife does not listen to me regarding this matter, for she claims that she wishes to follow the practice of all of the other Jews. However, she does wait approximately fifteen more minutes than the rest of the members of the community but she does not wait until the time of Rabbeinu Tam arrives. It turns out that I have actually written this pamphlet for myself (for only he would follow the stringency of Rabbeinu Tam) and I have only decided to publish it because I was told in a dream that it is a good thing for this pamphlet to be publicized, for as a result, many people will follow the opinion of Rabbeinu Tam and this may even hasten the Final Redemption.”
Many other great Poskim write likewise that anyone who is truly G-d-fearing should follow the stringency of Rabbeinu Tam and the majority of the Poskim and abstain from performing work on Motza’ei Shabbat until the time of Rabbeinu Tam; one should at least make an effort to follow this stringency with regards to abstaining from work prohibited by Torah law, such as turning on lights and the like. Indeed, Maran Shlit”a rules likewise although he usually tries to rule on halachic matters as leniently as possible, as he discusses at length in his Responsa Yabia Omer, Volume 2, Chapter 21. He would likewise bring this issue to people’s attention in his lectures, especially during the Ten Days of Repentance, where he would say that it is especially worthy to follow this stringency of Rabbeinu Tam all year round. In our times, many people indeed observe the stringency of Rabbeinu Tam, thank G-d.